The are many situations in which is necessary to extract a signal of interest from a noisy received signal. This task becomes harder in a situation in which the received signal has a low signal to noise ratio (SNR). In some cases, the signal of interest is generated in response to a stimulus. An example of such a case relates to the measurement of evoked responses. Electrophysiological evoked responses to a variety of stimuli are known to contain valuable clinical and scientific information in the assessment of the sensorineural systems of humans and animals. Evoked responses (ER), such as, for example, auditory evoked potentials, somatosensory evoked potentials, visual evoked potentials or otoacoustic emissions, are signals that are often 10-1000 times smaller than the noise that is typically recorded by signal transducers (such as electrodes or microphones) at the time of recording the ER. In many cases, the ER waveform and its clinically relevant features are only detectable after averaging thousands of responses to individual stimuli.
The noise that is recorded by the signal transducers may be from various sources, including, for example, noise generated by muscular activity (for example, EMS noise) during an evoked response (ER) test and may include other types of electrical noise from lighting, other instruments and the like. Because the noise is generally many times greater than the ER signal, the noise tends to mask the ER signal. One challenge of clinical ER measurement is determining whether specific features of an ER waveform represent true electrophysiological responses or if they are noise. A special application of ER detection is the detection of the auditory brainstem response (ABR) and auditory steady state responses with applications to infant hearing screening and to the determination of auditory thresholds, which may be used in the customized fitting of hearing aids. Detection of evoked responses may be performed manually by a clinician trained to recognize the ER waveform of interest or automatically with computer-based automated detection. In either case, detection is severely impaired by the presence of noise.
Automated response detection techniques include statistical methods and template matching methods. FSP is one statistical approach which uses a variance ratio to compare the signal estimate to the estimated averaged background noise (M. Don et al. “Objective Detection of Averaged Auditory Brainstem Responses” Scand Audiol. 1984; 13(4):219-28). Template matching methods detect the presence of a response by comparing the test waveform to another waveform previously learned by the system or acquired under similar conditions. There are also statistical techniques that use a priori knowledge of the waveform from a previously learned template to optimize the power of the statistical test (U.S. Pat. No. 6,196,917, Issue date: Mar. 6, 2001, Inventors: Yvonne S. Sininger, Martyn Hyde, Manuel Don).
Several techniques used to minimize noise in the recorded response to auditory stimuli are summarized in “M. Don and C. Elberling, Evaluating Residual Background Noise in Human Auditory Brain-Stem Responses, J. Acoust. Soc. Am. 96 (5), (1994)”. These techniques include signal averaging and weighted signal averaging, signal filtering, artifact rejection, and various techniques designed to relax or sedate the subject.
Signal averaging involves stimulating the patient with multiple stimuli, obtaining multiple time-based signal streams synchronized to the application of each of the multiple stimuli, and averaging the synchronized signal streams. Limitations of this traditional averaging method in evoked potential acquisition have long been recognized. The problem arises primarily from the poor signal to noise ratio (SNR) and the fact that the number of averages required, typically increases in inverse proportion to the square of the SNR. In a typical case of 10 microVolts of noise, to obtain a measurement of threshold-level auditory brainstem response of 100 nanoVolts with a modest SNR of 2:1 would require, on average, averaging responses to 40,000 stimuli. Under the constraint that the stimulus is not repeated until the response to the previous stimulus is received, there is an upper limit on the stimulus repetition rate. Furthermore, evoked responses may degrade when the stimulus repetition rate is too fast. In practical ABR screening systems, the stimulus repetition rate is limited to approximately 40 stimuli per second. More than 16 minutes would therefore be required to achieve a modest SNR of 2:1 in this example.
Artifact rejection (AR) can be used to eliminate epochs that are most contaminated with noise, by excluding those epochs for which the noise exceeds a preset threshold. Weighted averaging (WA) further improves SNR by weighting each epoch in inverse proportion to its noise content (see for example J. Sanchez and D. Gans, American Journal of Audiology Vol. 15 154-163, “Effects of Artifact Rejection and Bayesian Weighting on the Auditory Brainstem Response During Quiet and Active Behavioral Conditions”). Weighted averaging may be designed to optimize the SNR in the response by selecting weights according to Kalman Filter theory (J. Leski, “New concept of signal averaging in time domain”, Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 13:1, 1991, 367-368). This technique presumes an estimate of the error variance in the raw data. A variety of techniques for estimating error variance have been suggested in the prior art (see Jacek M. Leski, “Robust Weighted Averaging”, IEEE Transactions on Biomedical Engineering, V49:8, August 2002 and Li, Sokolov, Kunov, U.S. Pat. No. 7,286,983, “Signal and Method for Processing Low Signal-to-noise Ratio Signals”) but the inability to directly measure the error variance remains a drawback of the technique.
An important drawback of artifact rejection and weighted averaging is that when the noise is constantly present throughout the test, such as would be the case with an awake baby being tested for ABR, they are of limited use because equal amounts of signal and noise are removed.
Bandpass filtering may somewhat improve signal-to-noise ratio for detecting the low frequency components of some ERs, but is generally not helpful in the detection of the ABR, for example, since most of the ABR spectrum is contained within the same bandwidth as the EMG noise spectrum. For this reason, drug-induced sedation is usually required for ABR testing in babies and children from 6 months to 4 or 5 years of age (James Hall, New Handbook of Auditory Evoked Responses, Pearson Education Inc., 2007, p. 306). As will be understood the use of drug-induced sedation is preferably avoided.
Systems designed to detect and estimate ER signals, typically also estimate the noise (for example, the noise magnitude or the noise spectrum) contained in the estimated ER signal and the signal-to-noise ratio of the estimated ER signal. The estimated noise magnitude and signal-to-noise ratio may be conveyed to the user as an indication of confidence in the result. These estimates may be used in the calculation of test statistics to estimate the probability of the presence or absence of a response. The noise spectrum may be used to adaptively apply a filter that is optimized to eliminate the noise from the signal estimate.
One way to estimate the noise magnitude, used in the FSP technique cited above (M. Don et al., 1984) is to measure the variability of the recorded potential in all responses at a fixed latency relative to the stimulus. This technique provides a robust estimate of the noise magnitude but does not provide an estimate of the noise spectrum.
An estimate of the noise spectrum may be obtained from the spectrum during the prestimulus period (used in, for example, U.S. Pat. No. 5,230,344 Inventors Ozdamar, Ozcan and Delgado, Rafael E.). This technique has the disadvantage that the spectrum during the prestimulus period may not be identical to the noise spectrum that contaminates the ER signal and it may contain spectral components due to later latency responses.
One technique used to overcome this disadvantage is to transform the raw signal using a Discrete Fourier Transform (J. Fridman et al., Application of Digital Filtering and Automatic Peak Detection to Brainstem Auditory Evoked Potential, Electroencephalogy and Clinical Neurophysiology, 1982) and examining the phase coherence of each spectral component. Component that are more coherent are assumed to have a higher SNR than components that are less coherent. The disadvantage of this technique is that Fourier Transforms are not well suited to analyzing ER signals which, in general, are transient signals in which the magnitude and phase of individual components may vary within the analysis window.
This disadvantage was overcome with the introduction of the Complex Wavelet Transform (Arnaud Jacquin Elvir Causevic Roy John Jelena Kovacevic, “ADAPTIVE COMPLEX WAVELET-BASED FILTERING OF EEG FOR EXTRACTION OF EVOKED POTENTIAL”, ICASSP 2005) in which the phase coherence of each spectral component is used to assess that component's SNR. If the noise spectrum is variable (non-white) and differs significantly from the signal spectrum, eliminating or reducing incoherent components and applying the inverse transform to the data has been shown to improve signal to noise ratio better than conventional averaging. One disadvantage of this technique is that the phase coherence estimate is itself unreliable for low signal-to-noise ratio signals and must be based on a large number of averages to be reliable. Furthermore the repeated application of the complex wavelet transform is computationally far more complex than the Fourier Transform. Use of the relatively simpler Discrete Wavelet Transform could not be applied, since the transform components of the DWT are real values and do have a phase component.
One solution to this problem, presented by Causevic et al. (U.S. Pat. No. 7,333,619 “Fast wavelet estimation of weak bio-signals using novel algorithms for generating multiple additional data frames”) is to use a variable coherence threshold for the inclusion of discrete wavelet transform components in the signal. In this technique subaverages are created recursively in a binary tree structure (i.e. pairs of raw data frames are averaged and denoised to form a derived data frame, then pairs of those data frames are averaged and denoised to form the next level of data frames, etc.). For the purposes of this algorithm Causevic et al. defined coherence, not in terms of phase coherence which applies only to complex wavelet transforms as explained above, but rather in terms of the number of wavelet coefficients required to represent 99% of the signal. This approach has several apparent disadvantages recognized by Causevic et al. The signal being estimated must be coherent and smooth, when compared to the noise that corrupts it, i.e. it must be representable by relatively few wavelet coefficients because this is the basis of wavelet de-noising used by the authors. Secondly, the algorithm requires that all the frames of data be collected and stored prior to the application of the algorithm (i.e., for processing 512 frames, all of the 512 frames must be available in memory).
Another practice used to estimate the characteristics of the noise is to obtain multiple averages from independent sets of individual stimuli. The multiple averages may be collected sequentially or they may be obtained from interleaved data. Typically each response to each individual stimulus is assigned to one of two buffers designated Buffer A and Buffer B. Subsequent single-sweep responses are alternately assigned to a buffer, typically the odd-numbered responses in Buffer A and the even-numbered responses in Buffer B. The responses are combined with previous data in the assigned buffer using a conventional method such as for example averaging or weighted averaging. The spectrum and statistics of the waveform generated by subtracting the buffers (A−B in the typical case) then provides an estimate of the spectrum and statistics of the noise that contaminates the estimated ER signal. Alternatively the phase difference between the A and B spectra may be considered a measure of the phase coherence of each spectral component. The noise may be characterized as the variance of the (A−B)/2 buffer and SNR may be estimated as the variance ratio of the A+B to the A−B buffers. Furthermore, the coefficient of regression between buffers can be a measure of response repeatability and is related to the actual signal-to-noise ratio. The disadvantage of this method is that the estimate of A−B is unreliable and depends on the arbitrary assignment of raw data to buffers A and B. From a statistical perspective, the reliability of the estimate of the phase difference between A and B, will increase with the number of raw data frames used to generate A and B. The variance ratio used to estimate SNR, with the A−B variance in the denominator, is a poor estimator because degrees of freedom of this estimate is limited by relatively low number of cycles contained in the lowest frequency components in the estimate.
As such there is a need for improved systems and methods for processing and analysis of evoked responses.